The 2020 Chevalley Prize in Lie Theory will be awarded to Huanchen Bao and Weiqiang Wang for their fundamental contributions to the theory of quantum symmetric pairs.
This award is based on two publications: the paper "Canonical bases arising from quantum symmetric pairs," published in Inventiones Mathematicae, and the monograph "A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs," published in Astérisque. In these works, Huanchen Bao and Weiqiang Wang completely extended the known theory of canonical bases from the case of quantized enveloping algebras to the case of quantum symmetric pairs.
Response of Huanchen Bao and Weiqiang Wang:
We are extremely gratified and honored to receive the 2020 Chevalley Prize. We would like to thank George Lusztig for establishing the prize, whose groundbreaking works on Kazhdan-Lusztig theory and canonical bases form the central themes of our work in the cited papers.
When the senior prize recipient, Weiqiang Wang, was a PhD student under the supervision of V. Kac in the 1990s, character formulas for Lie superalgebras were largely unknown, not even conjecturally. A conceptual solution of the character formula problem for the Bernstein-Gelfand-Gelfand category of ortho-symplectic Lie superalgebras was given in the dissertation of the junior recipient, Huanchen Bao, two decades later.
To formulate the solution to the above problem and go beyond, we were led to develop a theory of canonical bases arising from quantum symmetric pairs, extending the canonical bases arising from quantum groups introduced by Lusztig. Our work was inspired by an earlier solution—due to Shun-Jen Cheng, Ngau Lam, and the senior recipient, Weiqiang Wang—of Jon Brundan's Kazhdan-Lusztig conjecture for general linear Lie superalgebras in terms of Lusztig's canonical basis.
The general theory of quantum symmetric pairs was formulated by Gail Letzter in the late 1990s and later extended by Stefan Kolb. The field is expanding rapidly in recent years thanks to the subsequent works of our friends and collaborators. We are very grateful to all of them, in particular to Yiqiang Li and Ming Lu, for what they have taught us. Huanchen Bao especially thanks his postdoc mentor, Xuhua He, for his guidance and encouragement.
Finally, we thank our families and friends for their support.
Biographical Sketch of Huanchen Bao:
Huanchen Bao is currently an assistant professor in the Department of Mathematics at the National University of Singapore. He was a postdoc at the University of Maryland, the Institute for Advanced Study (IAS), and the Max Planck Institute for Mathematics. (Photo courtesy of Lei Zhang.)
Biographical Sketch of Weiqiang Wang:
Weiqiang Wang is currently a professor of mathematics at the University of Virginia. He was a postdoc at IAS, Yale University, and the Max Planck Institute for Mathematics in Bonn. His research interest lies in representation theory, including Lie superalgebras, Hecke algebras, quantum groups, and connections to algebraic geometry. He enjoys collaborations and has learned much from his collaborators and students over the years.
About the Prize:
The Chevalley Prize is awarded in even-numbered years for notable work in Lie Theory published during the preceding six years; a recipient should be at most 25 years past the PhD. The prize was established in 2014 by George Lusztig to honor Claude Chevalley (1909-1984), a founding member of the Bourbaki group.